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There isn't anything built-in to either Evernote or Google Docs (now called "Google Drive") that will do a synchronization. Both services have an API so it would be possible for a third-party to build a synchronization tool.

One service which seems to do what you ask is cloudHQ. As of June 2012, this is a paid service which has a free option with limited functionality. The website says that the service will do a continuous real-time sync between Evernote and Google Drive. I have not used or ever tried the service. There is an (unanswered) question about cloudHQ at What format does cloudHQ backup Google Docs as? but I don't see any other questions on Stack Exchange about the service.

The closest to what you are looking for which I have used is a web service called ifttt ("if this then that") - it will let you create tasks which can be triggered by certain events or actions in various web services, so that an action may be executed on another web service when that event is detected.

For example, a task in ifttt might create a note in Evernote every time you star a document in Google Drive. This may help you to copy some data from one service to the other but it is not smart enough to do any synchronization logic.